*** Warning: There are a lot of generalizations following; my fellow Canadians, it's just an overview, not a perfect portrayal of our unique system ... pleae be kind ... ***
Okay, the Canadian system is different. Skate Canada skaters belong to a private club; for that privilege, we pay for ice time per session. You may generally only use the sessions you pay for (by season or annually). The qualification levels are specified, and the maximum number of skaters on the ice. The coaches are on contract to the club; only the coaches for that club, generally speaking, can step on the ice and coach on it. Coaches' contracts are renewed annually (or not, sometimes). The club may pay them for Canskate or group coaching, but, otherwise, they have no "pay" from the club. They are independent contractors, not employees.
The skaters pay for the ice time, and then they pay their coaches (by the way, how does it work if a skater in your commission system does like my guys do, working with, on some nights, 3 to 5 different coaches?
?).
If you want to work with a coach from a different club - you need to obtain a membership for that club, or pay "guest fees" on that club's sessions (i.e. get permission). There is usually a maximum number of guest skates per season, as they want the club members to have the benefit of being members. Coaches do not get involved with the payment of session fees to the club; it's up to the club to manage their ice time to maximize revenues and build skaters.
On occasion, coaches change clubs and often take their skaters with them; clubs can coax and wheedle a coach to come over to their club and bring their skaters (ethically coax and wheedle, of course). Some coaches are under contract to more than one club. It depends on how much time they want to spend coaching, etc etc etc.
The clubs take care of insurance, test days, registration, all of that. Skate Canada is our only governing body. If you want to compete: you have to belong to Skate Canada, and that means that you have to belong to a club of some sort or another. If you want more oddities ... clubs like Mariposa (elite training school, Jeff Buttle etc) - you skate there, but, have a membership at your home club, which you might never step on the ice at, so that you maintain your regional affiliation for qualifying competitions ...